Notebook: Modélisation GAMMs des diphtongues descendantes (/ai/, /au/, /ei/, /ou/) en mandarin standard
Chenyu LI
2022-02-22
This notebook is for the acoustic analysis of the falling diphthongs in the standard Mandarin with the approach GAMMs.
#install.packages('rmarkdown')# Importation des emballages
#install.packages("itsadug")
library(nlme)
library(ggplot2)
library(mgcv)## This is mgcv 1.8-33. For overview type 'help("mgcv-package")'.library(itsadug)## Loading required package: plotfunctions##
## Attaching package: 'plotfunctions'## The following object is masked from 'package:ggplot2':
##
## alpha## Loaded package itsadug 2.4 (see 'help("itsadug")' ).source("gamm_hacks.r")
#install.packages("tidyverse")
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──## ✓ tibble 3.1.0 ✓ dplyr 1.0.5
## ✓ tidyr 1.1.3 ✓ stringr 1.4.0
## ✓ readr 1.4.0 ✓ forcats 0.5.1
## ✓ purrr 0.3.4## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x plotfunctions::alpha() masks ggplot2::alpha()
## x dplyr::collapse() masks nlme::collapse()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()After the importation of the packages, let’s read the data.
# Importation des données
au <- read.table(file="au0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ai <- read.table(file="ai0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ei <- read.table(file="ei0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)
ou <- read.table(file="ou0a.tsv",sep="\t", fileEncoding = 'UTF-16', header = TRUE)Change of the nature of the variables in the dataset.
The criterion is that all the numerical variables are numerated and the string varibles are factored.
1 /ai/
Lets start from /ai/:
ai$sexe<-as.factor(ai$sexe)
ai$ton<-as.factor(ai$ton)
ai$pow<-as.factor(ai$pow)
ai$contexte.D<-as.factor(ai$contexte.D)
ai$contexte.G<-as.factor(ai$contexte.G)
ai$f1<-as.numeric(ai$f1)## Warning: NAs introduced by coercionai$f2<-as.numeric(ai$f2)## Warning: NAs introduced by coercionai$f3<-as.numeric(ai$f3)## Warning: NAs introduced by coercionai$f0<-as.numeric(ai$f0)## Warning: NAs introduced by coercionhead(ai)## numero sexe locuteur diphtongue ton pow contexte.G contexte.D duree.ms.
## 1 1 F FS11 ai 4 f h 0 102.6625
## 2 1 F FS11 ai 4 f h 0 102.6625
## 3 1 F FS11 ai 4 f h 0 102.6625
## 4 1 F FS11 ai 4 f h 0 102.6625
## 5 1 F FS11 ai 4 f h 0 102.6625
## 6 1 F FS11 ai 4 f h 0 102.6625
## measurement.no f1 f2 f3 f0
## 1 0 770.9403 1592.367 2791.365 242.7606
## 2 1 789.5770 1654.538 2661.433 232.8865
## 3 2 790.5264 1676.141 2643.341 228.2137
## 4 3 792.7979 1771.876 2587.896 224.4104
## 5 4 786.4961 1814.919 2436.698 219.7656
## 6 5 760.0966 1827.338 2542.548 214.1222In the dataset we can see the number of the data numero, the gender sexe, the speaker locuteur, the tone ton, the position in the word pow, the context before and after this diphthong contexte.G / contexte.D, the duration of the diphthongs duree.ms. and f0, f1, f2, f3 trajectories, each of them represented by 11 measurements taken at equal intervals (at 0%, 10%, 20%, . . . , 100%).
# Regroupement par les facteurs
ai.mas <- droplevels(subset(ai,sexe=="M"))
ai.fem <- droplevels(subset(ai,sexe=="F"))1.1 Masculin
1.1.1 F1
1.1.1.1 Basic models
Then the trajectories of f1 in different tones with regard of the sexes and the durations.
ggplot(ai.mas, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 28 row(s) containing missing values (geom_path).
ggplot(ai.fem, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 25 row(s) containing missing values (geom_path).
Then the first model with a basic smooth of tone 1 and difference smooths.
ai.mas$ton.ord <- as.ordered(ai.mas$ton)
contrasts(ai.mas$ton.ord) <- "contr.treatment"
ai.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 508.92 20.76 24.514 < 2e-16 ***
## ton.ord2 120.43 22.33 5.393 8.47e-08 ***
## ton.ord3 173.89 23.07 7.536 1.01e-13 ***
## ton.ord4 109.93 21.51 5.110 3.81e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.434 5.392 5.263 5.67e-05 ***
## s(measurement.no):ton.ord2 1.017 1.032 10.413 0.00111 **
## s(measurement.no):ton.ord3 1.001 1.002 4.728 0.02980 *
## s(measurement.no):ton.ord4 3.570 4.385 7.968 1.47e-06 ***Then the plots of predictions and difference smooth.
plot_smooth(ai.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 7.575758plot_diff(ai.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.323232 - 10.000000plot_diff(ai.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.929293
## 6.969697 - 10.000000The model that accounts for the influence of duree.ms. on the trajectories.
ai.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 521.48 20.47 25.471 < 2e-16 ***
## ton.ord2 96.33 22.45 4.291 1.94e-05 ***
## ton.ord3 174.32 22.42 7.777 1.74e-14 ***
## ton.ord4 97.59 21.32 4.578 5.25e-06 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.526 5.458 2.689 0.0153 *
## s(duree.ms.) 5.581 6.507 5.202 3.61e-05 ***
## ti(measurement.no,duree.ms.) 7.258 9.082 4.050 3.73e-05 ***
## s(measurement.no):ton.ord2 2.838 3.498 7.788 1.66e-05 ***
## s(measurement.no):ton.ord3 2.279 2.815 3.364 0.0173 *
## s(measurement.no):ton.ord4 4.009 4.879 6.286 1.52e-05 ***The plots with regard the durations.
plot_smooth(ai.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
ai.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 515.84 19.38 26.619 < 2e-16 ***
## ton.ord2 98.96 21.39 4.628 4.21e-06 ***
## ton.ord3 133.59 22.60 5.912 4.69e-09 ***
## ton.ord4 99.55 19.87 5.009 6.49e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.043 6.028 3.347 0.002781 **
## s(f0) 2.675 3.219 6.283 0.000272 ***
## ti(measurement.no,f0) 3.877 4.994 2.958 0.011798 *
## s(measurement.no):ton.ord2 3.114 3.839 7.162 2.42e-05 ***
## s(measurement.no):ton.ord3 2.262 2.803 6.325 0.000460 ***
## s(measurement.no):ton.ord4 4.213 5.118 8.474 < 2e-16 ***The plot of such model.
plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.1.1.2 extra models
# random intercepts only
ai.mas.gam.int <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr") +
s(numero, bs="re"),
data=ai.mas, method="fREML")
summary.coefs(ai.mas.gam.int)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 456.59 28.69 15.914 < 2e-16 ***
## ton.ord2 102.72 21.32 4.817 1.69e-06 ***
## ton.ord3 134.32 22.50 5.971 3.32e-09 ***
## ton.ord4 106.18 19.91 5.333 1.20e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.1635 6.149 3.407 0.002221 **
## s(f0) 2.7581 3.306 6.210 0.000251 ***
## ti(measurement.no,f0) 4.2159 5.440 2.916 0.011193 *
## s(measurement.no):ton.ord2 3.2824 4.041 7.045 1.4e-05 ***
## s(measurement.no):ton.ord3 2.5371 3.148 6.155 0.000312 ***
## s(measurement.no):ton.ord4 4.3255 5.243 8.514 < 2e-16 ***
## s(numero) 0.8844 1.000 7.653 0.003254 **plot_smooth(ai.mas.gam.int, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.mas.gam.int, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.mas.gam.int, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.mas.gam.int, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.mas.gam.int, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## fvisgam(ai.mas.gam.int, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
# random intercepts + slopes
ai.mas.gam.slope <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr") +
s(numero, bs="re") +
s(numero, measurement.no, bs="re"),
data=ai.mas, method="fREML")
summary.coefs(ai.mas.gam.slope)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 455.37 26.73 17.034 < 2e-16 ***
## ton.ord2 103.53 21.30 4.861 1.37e-06 ***
## ton.ord3 134.92 22.47 6.005 2.71e-09 ***
## ton.ord4 106.34 19.85 5.356 1.06e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.1531792 6.138 4.177 0.000328 ***
## s(f0) 2.7569210 3.305 6.089 0.000298 ***
## ti(measurement.no,f0) 4.1973202 5.423 2.853 0.012838 *
## s(measurement.no):ton.ord2 3.2594077 4.013 6.791 2.16e-05 ***
## s(measurement.no):ton.ord3 2.5316088 3.141 6.168 0.000308 ***
## s(measurement.no):ton.ord4 4.3419115 5.262 8.353 < 2e-16 ***
## s(numero) 0.0002281 1.000 0.000 0.606058
## s(numero,measurement.no) 0.9128615 1.000 10.485 0.000716 ***plot_smooth(ai.mas.gam.slope, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.mas.gam.slope, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.mas.gam.slope, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.mas.gam.slope, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.mas.gam.slope, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## fvisgam(ai.mas.gam.slope, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
plot_smooth(ai.mas.gam.slope, view="measurement.no", plot_all="ton.ord",
rug=F, rm.ranef=T)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 137.402261031236.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## 
#plot_diff(ai.mas.gam.slope, view="measurement.no",
#comp=list(ton.ord = c("2","4")), rm.ranef=T)#ai.mas.gam.smooth <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
# s(f0, bs="cr") +
# ti(measurement.no, f0) +
# s(measurement.no, by=ton.ord, bs="cr") +
# s(measurement.no, numero, bs="fs", xt="cr", m=1, k=5),
# data=ai.mas, method="fREML")
#summary.coefs(ai.mas.gam.smooth)ai.mas$start.event <- ai.mas$measurement.no==0
r1 <- start_value_rho(ai.mas.gam.f0)
ai.mas.gam.AR <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="fREML",
rho=r1, AR.start=ai.mas$start.event)
summary.coefs(ai.mas.gam.AR)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 528.66 28.03 18.858 < 2e-16 ***
## ton.ord2 91.67 30.74 2.982 0.002937 **
## ton.ord3 115.66 32.36 3.574 0.000369 ***
## ton.ord4 85.10 28.73 2.961 0.003137 **
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 6.036 7.043 3.644 0.000664 ***
## s(f0) 1.878 2.303 2.973 0.056214 .
## ti(measurement.no,f0) 4.238 5.488 2.497 0.025727 *
## s(measurement.no):ton.ord2 3.946 4.932 6.458 9.21e-06 ***
## s(measurement.no):ton.ord3 3.172 4.024 4.928 0.000613 ***
## s(measurement.no):ton.ord4 5.015 6.080 7.806 < 2e-16 ***plot_smooth(ai.mas.gam.AR, view="measurement.no", plot_all="ton.ord",
rug=F, rm.ranef=T)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 137.402261031236.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.mas.gam.AR, view="measurement.no",
comp=list(ton.ord = c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 137.402261031236.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 1.515152plot_smooth(ai.mas.gam.AR, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.AR, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.AR, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.AR, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.gam.AR, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.gam.AR, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.1.1.3 Central portion
We now focus on the central portion of the diphthongs, which means the portions without the inluence of the consonant contexts.
ai.central<-droplevels(subset(ai,measurement.no>=2))
ai.central<-droplevels(subset(ai.central,measurement.no<=8))
ai.central.mas <- droplevels(subset(ai.central,sexe=="M"))
ai.central.fem <- droplevels(subset(ai.central,sexe=="F"))ai.central.mas$ton.ord <- as.ordered(ai.central.mas$ton)
contrasts(ai.central.mas$ton.ord) <- "contr.treatment"
ai.central.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 472.08 19.51 24.201 < 2e-16 ***
## ton.ord2 171.54 20.96 8.184 1.28e-15 ***
## ton.ord3 225.45 21.68 10.399 < 2e-16 ***
## ton.ord4 187.63 20.19 9.292 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.404 2.924 9.433 1.01e-05 ***
## s(measurement.no):ton.ord2 1.002 1.004 0.147 0.7039
## s(measurement.no):ton.ord3 1.002 1.005 1.309 0.2530
## s(measurement.no):ton.ord4 2.529 3.067 2.551 0.0533 .plot_smooth(ai.central.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 8.000000plot_diff(ai.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.848485 - 8.000000plot_diff(ai.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 3.030303
## 5.818182 - 8.000000ai.central.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 483.05 19.43 24.864 < 2e-16 ***
## ton.ord2 153.92 21.26 7.239 1.19e-12 ***
## ton.ord3 225.56 21.26 10.609 < 2e-16 ***
## ton.ord4 175.66 20.20 8.697 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.393 2.910 10.314 3.87e-06 ***
## s(duree.ms.) 4.484 4.852 4.597 0.000297 ***
## ti(measurement.no,duree.ms.) 1.236 1.431 5.669 0.006689 **
## s(measurement.no):ton.ord2 1.000 1.000 0.094 0.759550
## s(measurement.no):ton.ord3 1.000 1.001 1.487 0.223105
## s(measurement.no):ton.ord4 2.587 3.131 2.965 0.029587 *plot_smooth(ai.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.central.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.central.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 480.55 18.43 26.068 < 2e-16 ***
## ton.ord2 159.40 20.21 7.886 1.3e-14 ***
## ton.ord3 182.35 21.24 8.583 < 2e-16 ***
## ton.ord4 178.19 18.85 9.455 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.449 2.975 7.785 5.8e-05 ***
## s(f0) 2.888 3.362 5.997 0.000297 ***
## ti(measurement.no,f0) 1.005 1.010 6.139 0.013357 *
## s(measurement.no):ton.ord2 1.000 1.000 0.233 0.629530
## s(measurement.no):ton.ord3 1.000 1.001 0.006 0.938828
## s(measurement.no):ton.ord4 2.698 3.256 2.878 0.031657 *plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.central.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 99.155553 to 204.798228.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.1.2 F2
1.1.2.1 Basic models
Now we look at the trajectories of f2 in different tones with regard of the sexes and the durations.
ggplot(ai.mas, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 28 row(s) containing missing values (geom_path).
ggplot(ai.fem, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 25 row(s) containing missing values (geom_path).
Then we fit the same model with a basic smooth of tone 1 and difference smooths.
ai.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1808.78 25.76 70.213 < 2e-16 ***
## ton.ord2 -190.78 27.71 -6.885 9.73e-12 ***
## ton.ord3 -182.21 28.63 -6.364 2.89e-10 ***
## ton.ord4 -157.18 26.70 -5.887 5.22e-09 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 3.783 4.654 6.929 7.58e-06 ***
## s(measurement.no):ton.ord2 1.000 1.001 0.783 0.376
## s(measurement.no):ton.ord3 1.001 1.001 0.225 0.635
## s(measurement.no):ton.ord4 1.004 1.008 0.360 0.550Now the plots of f2 with different tones.
plot_smooth(ai.mas.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 10.000000plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.020202plot_diff(ai.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 5.252525 - 10.000000The model that accounts for the influence of duree.ms. on the trajectories.
ai.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1826.36 25.30 72.182 < 2e-16 ***
## ton.ord2 -210.79 27.64 -7.627 5.22e-14 ***
## ton.ord3 -190.56 27.77 -6.861 1.15e-11 ***
## ton.ord4 -178.75 26.32 -6.793 1.81e-11 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 3.893 4.783 8.213 6.26e-07 ***
## s(duree.ms.) 3.903 4.707 5.118 0.000252 ***
## ti(measurement.no,duree.ms.) 2.869 4.012 12.552 < 2e-16 ***
## s(measurement.no):ton.ord2 1.001 1.002 1.332 0.248618
## s(measurement.no):ton.ord3 1.001 1.003 0.351 0.553691
## s(measurement.no):ton.ord4 1.001 1.003 0.038 0.847241The plots with regard the durations.
plot_smooth(ai.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.mas, method="ML")
summary.coefs(ai.mas.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1809.15 24.68 73.316 < 2e-16 ***
## ton.ord2 -187.20 27.28 -6.862 1.21e-11 ***
## ton.ord3 -201.12 28.74 -6.999 4.80e-12 ***
## ton.ord4 -156.85 25.33 -6.191 8.79e-10 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.100 5.036 9.733 < 2e-16 ***
## s(f0) 5.833 6.673 5.023 2.82e-05 ***
## ti(measurement.no,f0) 2.307 2.805 2.708 0.0422 *
## s(measurement.no):ton.ord2 1.001 1.002 0.005 0.9472
## s(measurement.no):ton.ord3 1.001 1.001 0.034 0.8553
## s(measurement.no):ton.ord4 1.004 1.008 0.011 0.9373plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.mas.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.1.2.2 extra models
# random intercepts only
ai.mas.gam.f2.int <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr") +
s(numero, bs="re"),
data=ai.mas, method="fREML")
summary.coefs(ai.mas.gam.f2.int)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1809.17 24.68 73.315 < 2e-16 ***
## ton.ord2 -187.22 27.28 -6.863 1.20e-11 ***
## ton.ord3 -201.16 28.74 -7.000 4.76e-12 ***
## ton.ord4 -156.88 25.33 -6.192 8.74e-10 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.127e+00 5.067 9.697 < 2e-16 ***
## s(f0) 5.824e+00 6.663 5.023 2.86e-05 ***
## ti(measurement.no,f0) 2.327e+00 2.827 2.705 0.0422 *
## s(measurement.no):ton.ord2 1.000e+00 1.000 0.005 0.9413
## s(measurement.no):ton.ord3 1.000e+00 1.000 0.034 0.8542
## s(measurement.no):ton.ord4 1.000e+00 1.000 0.011 0.9171
## s(numero) 2.024e-05 1.000 0.000 0.6922plot_smooth(ai.mas.gam.f2.int, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.mas.gam.f2.int, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.mas.gam.f2.int, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.mas.gam.f2.int, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.mas.gam.f2.int, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## fvisgam(ai.mas.gam.f2.int, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
# random intercepts + slopes
ai.mas.gam.f2.slope <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr") +
s(numero, bs="re") +
s(numero, measurement.no, bs="re"),
data=ai.mas, method="fREML")
summary.coefs(ai.mas.gam.f2.slope)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1783.01 31.63 56.364 < 2e-16 ***
## ton.ord2 -185.70 27.28 -6.806 1.75e-11 ***
## ton.ord3 -200.83 28.72 -6.994 4.98e-12 ***
## ton.ord4 -154.22 25.39 -6.073 1.80e-09 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.124e+00 5.064 7.800 4.40e-07 ***
## s(f0) 5.768e+00 6.604 4.719 6.49e-05 ***
## ti(measurement.no,f0) 2.322e+00 2.822 2.658 0.0451 *
## s(measurement.no):ton.ord2 1.000e+00 1.000 0.022 0.8812
## s(measurement.no):ton.ord3 1.000e+00 1.000 0.024 0.8774
## s(measurement.no):ton.ord4 1.000e+00 1.001 0.033 0.8568
## s(numero) 3.609e-05 1.000 0.000 0.4983
## s(numero,measurement.no) 6.351e-01 1.000 1.741 0.0975 .plot_smooth(ai.mas.gam.f2.slope, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.mas.gam.f2.slope, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.mas.gam.f2.slope, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.mas.gam.f2.slope, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.mas.gam.f2.slope, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## fvisgam(ai.mas.gam.f2.slope, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
plot_smooth(ai.mas.gam.f2.slope, view="measurement.no", plot_all="ton.ord",
rug=F, rm.ranef=T)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 137.402261031236.
## * numero : numeric predictor; set to the value(s): 164. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## 
#plot_diff(ai.mas.gam.slope, view="measurement.no",
#comp=list(ton.ord = c("2","4")), rm.ranef=T)#ai.mas.gam.f2.smooth <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
# s(f0, bs="cr") +
# ti(measurement.no, f0) +
# s(measurement.no, by=ton.ord, bs="cr") +
# s(measurement.no, numero, bs="fs", xt="cr", m=1, k=5),
# data=ai.mas, method="fREML")
#summary.coefs(ai.mas.gam.f2.smooth)1.1.2.3 Central portion
The central portion:
ai.central.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1797.78 28.10 63.974 < 2e-16 ***
## ton.ord2 -169.65 30.20 -5.618 2.77e-08 ***
## ton.ord3 -154.65 31.23 -4.952 9.20e-07 ***
## ton.ord4 -136.24 29.09 -4.683 3.38e-06 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.005 1.011 7.229 0.00732 **
## s(measurement.no):ton.ord2 1.001 1.002 0.268 0.60543
## s(measurement.no):ton.ord3 1.001 1.002 0.035 0.85460
## s(measurement.no):ton.ord4 1.001 1.003 0.595 0.44147plot_smooth(ai.central.mas.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 8.000000plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 6.242424 - 8.000000plot_diff(ai.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.939394 - 7.454545ai.central.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1809.11 27.47 65.867 < 2e-16 ***
## ton.ord2 -178.42 29.78 -5.992 3.30e-09 ***
## ton.ord3 -158.81 30.29 -5.243 2.09e-07 ***
## ton.ord4 -152.09 28.53 -5.331 1.32e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.106 1.204 6.368 0.01168 *
## s(duree.ms.) 2.613 3.155 4.432 0.00315 **
## ti(measurement.no,duree.ms.) 3.274 4.240 7.847 2.48e-06 ***
## s(measurement.no):ton.ord2 1.001 1.002 1.433 0.23173
## s(measurement.no):ton.ord3 1.001 1.002 0.023 0.88142
## s(measurement.no):ton.ord4 1.002 1.003 0.342 0.56017plot_smooth(ai.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.central.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 80.084553 to 197.994270.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.central.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.mas, method="ML")
summary.coefs(ai.central.mas.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1808.72 25.82 70.057 < 2e-16 ***
## ton.ord2 -183.71 28.33 -6.485 1.74e-10 ***
## ton.ord3 -198.13 29.76 -6.658 5.86e-11 ***
## ton.ord4 -147.99 26.51 -5.582 3.48e-08 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.001 1.002 9.506 0.00212 **
## s(f0) 4.105 4.579 7.115 2.97e-06 ***
## ti(measurement.no,f0) 5.049 5.936 5.348 2.37e-05 ***
## s(measurement.no):ton.ord2 1.001 1.001 0.421 0.51700
## s(measurement.no):ton.ord3 1.001 1.001 0.465 0.49561
## s(measurement.no):ton.ord4 1.001 1.001 0.610 0.43499plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.mas.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.central.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 99.155553 to 204.798228.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.2 Féminin
1.2.1 F1
1.2.1.1 Basic models
We now switch to the data of feminin subjects.
The first model with a basic smooth of tone 1 and difference smooths.
ai.fem$ton.ord <- as.ordered(ai.fem$ton)
contrasts(ai.fem$ton.ord) <- "contr.treatment"
ai.fem.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 727.300 10.502 69.251 < 2e-16 ***
## ton.ord2 41.824 12.745 3.282 0.00106 **
## ton.ord3 9.285 13.129 0.707 0.47957
## ton.ord4 -4.129 11.138 -0.371 0.71090
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.990 6.014 22.139 < 2e-16 ***
## s(measurement.no):ton.ord2 1.976 2.459 3.589 0.02225 *
## s(measurement.no):ton.ord3 1.004 1.008 4.710 0.03005 *
## s(measurement.no):ton.ord4 2.916 3.598 4.183 0.00373 **Then the plots of predictions and difference smooth.
plot_smooth(ai.fem.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 4.343434plot_diff(ai.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.323232
## 7.777778 - 10.000000plot_diff(ai.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.828283
## 6.161616 - 7.676768The model that accounts for the influence of duree.ms. on the trajectories.
ai.fem.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 725.48603 10.51394 69.002 < 2e-16 ***
## ton.ord2 38.51010 12.39140 3.108 0.00193 **
## ton.ord3 9.42465 13.15220 0.717 0.47377
## ton.ord4 0.02272 11.37780 0.002 0.99841
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.275 6.330 25.533 < 2e-16 ***
## s(duree.ms.) 7.132 8.041 6.159 < 2e-16 ***
## ti(measurement.no,duree.ms.) 8.571 10.747 5.436 < 2e-16 ***
## s(measurement.no):ton.ord2 2.039 2.534 3.642 0.01899 *
## s(measurement.no):ton.ord3 1.007 1.012 10.009 0.00158 **
## s(measurement.no):ton.ord4 2.434 3.015 2.159 0.09079 .The plots with regard the durations.
plot_smooth(ai.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 89.970028 to 186.666330.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
ai.fem.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 726.023 10.603 68.474 <2e-16 ***
## ton.ord2 36.953 14.222 2.598 0.0095 **
## ton.ord3 15.256 14.126 1.080 0.2804
## ton.ord4 -2.092 11.020 -0.190 0.8494
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.092 6.142 32.725 < 2e-16 ***
## s(f0) 1.000 1.000 1.679 0.195397
## ti(measurement.no,f0) 2.285 2.770 5.741 0.000985 ***
## s(measurement.no):ton.ord2 1.000 1.001 0.466 0.495028
## s(measurement.no):ton.ord3 1.000 1.001 0.245 0.620400
## s(measurement.no):ton.ord4 2.564 3.184 3.425 0.015002 *The plot of such model.
plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.611858 to 275.883293.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.2.1.2 extra models
# random intercepts only
ai.fem.gam.int <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr") +
s(numero, bs="re"),
data=ai.fem, method="fREML")
summary.coefs(ai.fem.gam.int)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 748.285 11.493 65.107 <2e-16 ***
## ton.ord2 35.242 14.163 2.488 0.013 *
## ton.ord3 21.055 14.126 1.490 0.136
## ton.ord4 1.546 11.010 0.140 0.888
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.1331 6.184 32.528 < 2e-16 ***
## s(f0) 1.0000 1.000 1.098 0.29484
## ti(measurement.no,f0) 3.5799 4.896 3.511 0.00416 **
## s(measurement.no):ton.ord2 1.0001 1.000 0.150 0.69866
## s(measurement.no):ton.ord3 1.0003 1.001 0.124 0.72537
## s(measurement.no):ton.ord4 2.6626 3.295 3.625 0.01065 *
## s(numero) 0.9609 1.000 24.572 7.72e-07 ***plot_smooth(ai.fem.gam.int, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.fem.gam.int, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.fem.gam.int, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.fem.gam.int, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## plot_smooth(ai.fem.gam.int, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## fvisgam(ai.fem.gam.int, view=c("measurement.no","f0"),
ylim=quantile(ai.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 100.125696 to 212.400605.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero)
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
# random intercepts + slopes
ai.fem.gam.slope <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr") +
s(numero, bs="re") +
s(numero, measurement.no, bs="re"),
data=ai.fem, method="fREML")
summary.coefs(ai.fem.gam.slope)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 747.286 11.407 65.514 <2e-16 ***
## ton.ord2 36.487 14.158 2.577 0.0101 *
## ton.ord3 21.379 14.114 1.515 0.1301
## ton.ord4 1.958 11.003 0.178 0.8588
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.1283 6.178 30.085 < 2e-16 ***
## s(f0) 1.0001 1.000 1.323 0.25034
## ti(measurement.no,f0) 3.4752 4.757 3.598 0.00400 **
## s(measurement.no):ton.ord2 1.0002 1.000 0.156 0.69325
## s(measurement.no):ton.ord3 1.0003 1.001 0.034 0.85413
## s(measurement.no):ton.ord4 2.6666 3.300 3.757 0.00877 **
## s(numero) 0.6759 1.000 5.927 0.07910 .
## s(numero,measurement.no) 0.8148 1.000 12.630 0.02023 *plot_smooth(ai.fem.gam.slope, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.fem.gam.slope, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.fem.gam.slope, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.fem.gam.slope, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## plot_smooth(ai.fem.gam.slope, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## fvisgam(ai.fem.gam.slope, view=c("measurement.no","f0"),
ylim=quantile(ai.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.611858 to 275.883293.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
plot_smooth(ai.fem.gam.slope, view="measurement.no", plot_all="ton.ord",
rug=F, rm.ranef=T)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 203.561992329367.
## * numero : numeric predictor; set to the value(s): 57. (Might be canceled as random effect, check below.)
## * NOTE : The following random effects columns are canceled: s(numero),s(numero,measurement.no)
## 
#plot_diff(ai.mas.gam.slope, view="measurement.no",
#comp=list(ton.ord = c("2","4")), rm.ranef=T)#ai.fem.gam.smooth <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
# s(f0, bs="cr") +
# ti(measurement.no, f0) +
# s(measurement.no, by=ton.ord, bs="cr") +
# s(measurement.no, numero, bs="fs", xt="cr", m=1, k=5),
# data=ai.fem, method="fREML")
#summary.coefs(ai.fem.gam.smooth)ai.fem$start.event <- ai.fem$measurement.no==0
r1 <- start_value_rho(ai.fem.gam.f0)
ai.fem.gam.AR <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="fREML",
rho=r1, AR.start=ai.fem$start.event)
summary.coefs(ai.fem.gam.AR)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 730.847 17.036 42.901 <2e-16 ***
## ton.ord2 44.139 22.273 1.982 0.0478 *
## ton.ord3 8.903 22.447 0.397 0.6917
## ton.ord4 -4.354 17.857 -0.244 0.8074
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 6.289 7.490 24.971 < 2e-16 ***
## s(f0) 1.000 1.000 0.669 0.413682
## ti(measurement.no,f0) 4.329 5.818 4.314 0.000372 ***
## s(measurement.no):ton.ord2 1.000 1.000 0.805 0.369761
## s(measurement.no):ton.ord3 1.000 1.001 0.385 0.535005
## s(measurement.no):ton.ord4 3.102 3.972 3.223 0.013040 *plot_smooth(ai.fem.gam.AR, view="measurement.no", plot_all="ton.ord",
rug=F, rm.ranef=T)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 203.561992329367.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.fem.gam.AR, view="measurement.no",
comp=list(ton.ord = c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 203.561992329367.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 3.939394
## 7.575758 - 10.000000plot_smooth(ai.fem.gam.AR, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.AR, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.AR, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.AR, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.gam.AR, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.gam.AR, view=c("measurement.no","f0"),
ylim=quantile(ai.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.611858 to 275.883293.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.2.1.3 Central portion
We now focus on the central portion of the diphthongs, which means the portions without the inluence of the consonant contexts.
ai.central.fem$ton.ord <- as.ordered(ai.central.fem$ton)
contrasts(ai.central.fem$ton.ord) <- "contr.treatment"
ai.central.fem.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 764.464 10.337 73.951 <2e-16 ***
## ton.ord2 23.456 12.626 1.858 0.0636 .
## ton.ord3 1.278 13.036 0.098 0.9219
## ton.ord4 6.941 10.981 0.632 0.5275
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.787 3.350 9.759 1.85e-06 ***
## s(measurement.no):ton.ord2 1.002 1.005 3.192 0.0744 .
## s(measurement.no):ton.ord3 1.002 1.005 5.494 0.0192 *
## s(measurement.no):ton.ord4 2.339 2.843 2.021 0.1193plot_smooth(ai.central.fem.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 4.848485plot_diff(ai.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 4.787879 - 7.090909plot_diff(ai.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 2.969697
## 5.151515 - 8.000000ai.central.fem.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 765.093 10.573 72.362 <2e-16 ***
## ton.ord2 24.013 12.492 1.922 0.055 .
## ton.ord3 -2.690 13.290 -0.202 0.840
## ton.ord4 6.656 11.439 0.582 0.561
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.800 3.363 10.238 9.86e-07 ***
## s(duree.ms.) 4.244 4.713 3.477 0.0354 *
## ti(measurement.no,duree.ms.) 2.227 2.802 2.612 0.0375 *
## s(measurement.no):ton.ord2 1.001 1.002 3.054 0.0809 .
## s(measurement.no):ton.ord3 1.001 1.002 5.522 0.0190 *
## s(measurement.no):ton.ord4 2.354 2.860 2.097 0.1080plot_smooth(ai.central.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.fem.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.central.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 89.970028 to 186.666330.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.central.fem.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 753.01 10.66 70.639 <2e-16 ***
## ton.ord2 40.34 14.26 2.829 0.0048 **
## ton.ord3 25.36 14.31 1.771 0.0769 .
## ton.ord4 14.76 11.07 1.333 0.1828
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.956 3.535 12.622 < 2e-16 ***
## s(f0) 1.000 1.001 9.090 0.00265 **
## ti(measurement.no,f0) 1.003 1.006 7.019 0.00817 **
## s(measurement.no):ton.ord2 1.001 1.002 1.025 0.31201
## s(measurement.no):ton.ord3 1.001 1.001 1.560 0.21208
## s(measurement.no):ton.ord4 2.117 2.590 1.603 0.18325plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.fem.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.central.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.333410 to 268.051028.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.2.2 F2
1.2.2.1 Basic models
We fit the same model with a basic smooth of tone 1 and difference smooths.
ai.fem.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2038.36 17.15 118.880 < 2e-16 ***
## ton.ord2 -107.98 20.81 -5.189 2.49e-07 ***
## ton.ord3 -88.98 21.43 -4.152 3.53e-05 ***
## ton.ord4 -70.79 18.18 -3.893 0.000105 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.280 5.234 3.945 0.001255 **
## s(measurement.no):ton.ord2 1.002 1.005 22.811 2.65e-06 ***
## s(measurement.no):ton.ord3 2.149 2.673 9.920 9.98e-06 ***
## s(measurement.no):ton.ord4 1.003 1.005 11.113 0.000866 ***Now the plots of f2 with different tones.
plot_smooth(ai.fem.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 6.666667plot_diff(ai.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 4.545455 - 5.959596plot_diff(ai.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.424242The model that accounts for the influence of duree.ms. on the trajectories.
ai.fem.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2038.81 17.36 117.410 < 2e-16 ***
## ton.ord2 -102.76 20.46 -5.023 5.88e-07 ***
## ton.ord3 -87.08 21.69 -4.014 6.35e-05 ***
## ton.ord4 -73.67 18.78 -3.922 9.29e-05 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.356 5.321 4.858 0.000157 ***
## s(duree.ms.) 6.537 7.514 5.600 1.96e-06 ***
## ti(measurement.no,duree.ms.) 3.189 3.659 7.475 1.13e-05 ***
## s(measurement.no):ton.ord2 1.002 1.005 21.541 3.84e-06 ***
## s(measurement.no):ton.ord3 2.182 2.713 8.207 6.17e-05 ***
## s(measurement.no):ton.ord4 1.004 1.007 4.444 0.034836 *The plots with regard the durations.
plot_smooth(ai.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 89.970028 to 186.666330.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.fem.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ai.fem, method="ML")
summary.coefs(ai.fem.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2006.20 17.59 114.025 <2e-16 ***
## ton.ord2 -47.56 23.69 -2.008 0.0449 *
## ton.ord3 -39.15 23.59 -1.660 0.0972 .
## ton.ord4 -33.95 18.66 -1.819 0.0691 .
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 3.765 4.647 3.339 0.006051 **
## s(f0) 4.465 5.325 9.702 < 2e-16 ***
## ti(measurement.no,f0) 1.001 1.002 3.953 0.046912 *
## s(measurement.no):ton.ord2 1.000 1.001 7.075 0.007921 **
## s(measurement.no):ton.ord3 1.878 2.345 4.999 0.004516 **
## s(measurement.no):ton.ord4 1.001 1.002 14.369 0.000158 ***plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.fem.f2.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.fem.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.611858 to 275.883293.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
1.2.2.2 Central portion
The central portion:
ai.central.fem.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2048.03 17.96 114.046 < 2e-16 ***
## ton.ord2 -110.36 21.93 -5.032 6.06e-07 ***
## ton.ord3 -68.99 22.65 -3.047 0.00239 **
## ton.ord4 -74.75 19.08 -3.919 9.70e-05 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.354 1.610 3.247 0.03218 *
## s(measurement.no):ton.ord2 1.002 1.003 7.512 0.00623 **
## s(measurement.no):ton.ord3 1.002 1.004 6.353 0.01188 *
## s(measurement.no):ton.ord4 1.108 1.194 1.388 0.20091plot_smooth(ai.central.fem.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ai.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 6.727273plot_diff(ai.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.757576 - 5.818182plot_diff(ai.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(ai.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 5.333333ai.central.fem.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2057.82 18.18 113.168 < 2e-16 ***
## ton.ord2 -114.28 21.48 -5.321 1.36e-07 ***
## ton.ord3 -74.34 22.87 -3.251 0.0012 **
## ton.ord4 -88.36 19.67 -4.491 8.18e-06 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.226 1.395 6.156 0.005088 **
## s(duree.ms.) 4.351 4.781 5.615 0.000994 ***
## ti(measurement.no,duree.ms.) 2.317 2.905 5.698 0.001249 **
## s(measurement.no):ton.ord2 1.001 1.002 7.310 0.006986 **
## s(measurement.no):ton.ord3 1.001 1.002 4.581 0.032602 *
## s(measurement.no):ton.ord4 1.276 1.479 0.171 0.687964plot_smooth(ai.central.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.fem.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ai.central.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 89.970028 to 186.666330.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ai.central.fem.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=ai.central.fem, method="ML")
summary.coefs(ai.central.fem.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2010.59 18.67 107.680 <2e-16 ***
## ton.ord2 -46.55 25.44 -1.830 0.0677 .
## ton.ord3 -24.49 25.01 -0.979 0.3278
## ton.ord4 -31.78 19.74 -1.610 0.1079
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.019 1.036 9.108 0.00263 **
## s(f0) 3.656 4.215 12.066 < 2e-16 ***
## ti(measurement.no,f0) 2.960 3.539 4.413 0.00284 **
## s(measurement.no):ton.ord2 1.001 1.001 2.724 0.09917 .
## s(measurement.no):ton.ord3 1.001 1.001 2.309 0.12896
## s(measurement.no):ton.ord4 1.158 1.296 1.005 0.41341plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ai.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ai.central.fem.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ai.central.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 159.333410 to 268.051028.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2 /au/
The next diphthong we look at is /au/.
au$sexe<-as.factor(au$sexe)
au$ton<-as.factor(au$ton)
au$pow<-as.factor(au$pow)
au$contexte.D<-as.factor(au$contexte.D)
au$contexte.G<-as.factor(au$contexte.G)
au$f1<-as.numeric(au$f1)## Warning: NAs introduced by coercionau$f2<-as.numeric(au$f2)## Warning: NAs introduced by coercionau$f3<-as.numeric(au$f3)## Warning: NAs introduced by coercionau$f0<-as.numeric(au$f0)## Warning: NAs introduced by coercion# Regroupement par les facteurs
au.mas <- droplevels(subset(au,sexe=="M"))
au.fem <- droplevels(subset(au,sexe=="F"))2.1 Masculin
2.1.1 F1
Then the trajectories of f1 in different tones with regard of the sexes and the durations.
ggplot(au.mas, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 28 row(s) containing missing values (geom_path).
ggplot(au.fem, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 5 row(s) containing missing values (geom_path).
2.1.1.1 Basic models
Then the first model with a basic smooth of tone 1 and difference smooths.
au.mas$ton.ord <- as.ordered(au.mas$ton)
contrasts(au.mas$ton.ord) <- "contr.treatment"
au.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 526.114 9.404 55.95 < 2e-16 ***
## ton.ord2 126.252 15.586 8.10 1.4e-15 ***
## ton.ord3 126.917 11.210 11.32 < 2e-16 ***
## ton.ord4 114.900 9.973 11.52 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.175 6.240 43.623 <2e-16 ***
## s(measurement.no):ton.ord2 1.001 1.003 1.017 0.3133
## s(measurement.no):ton.ord3 1.001 1.003 0.047 0.8300
## s(measurement.no):ton.ord4 1.002 1.004 6.038 0.0141 *Then the plots of predictions and difference smooth.
plot_smooth(au.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 10.000000plot_diff(au.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.plot_diff(au.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 4.646465The model that accounts for the influence of duree.ms. on the trajectories.
au.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 524.641 9.171 57.206 < 2e-16 ***
## ton.ord2 125.207 15.416 8.122 1.2e-15 ***
## ton.ord3 126.015 10.888 11.574 < 2e-16 ***
## ton.ord4 117.901 9.772 12.065 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.187 6.250 29.289 < 2e-16 ***
## s(duree.ms.) 5.773 6.746 6.298 1.86e-06 ***
## ti(measurement.no,duree.ms.) 4.795 6.455 4.367 0.000185 ***
## s(measurement.no):ton.ord2 1.002 1.004 1.567 0.210558
## s(measurement.no):ton.ord3 1.002 1.003 0.036 0.852676
## s(measurement.no):ton.ord4 1.404 1.692 3.803 0.063064 .The plots with regard the durations.
plot_smooth(au.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 88.249203 to 188.623093.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
au.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 529.26 10.05 52.638 < 2e-16 ***
## ton.ord2 131.08 15.62 8.395 < 2e-16 ***
## ton.ord3 95.77 13.39 7.155 1.74e-12 ***
## ton.ord4 101.76 10.81 9.413 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.252 6.333 33.975 < 2e-16 ***
## s(f0) 4.586 5.322 6.824 2.52e-06 ***
## ti(measurement.no,f0) 7.991 9.443 6.179 < 2e-16 ***
## s(measurement.no):ton.ord2 1.001 1.001 0.432 0.5114
## s(measurement.no):ton.ord3 1.001 1.001 3.349 0.0676 .
## s(measurement.no):ton.ord4 1.001 1.002 0.611 0.4344The plot of such model.
plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 96.765573 to 193.084157.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2.1.1.2 Central portion
We now focus on the central portion of the diphthongs, which means the portions without the inluence of the consonant contexts.
au.central<-droplevels(subset(au,measurement.no>=2))
au.central<-droplevels(subset(au.central,measurement.no<=8))
au.central.mas <- droplevels(subset(au.central,sexe=="M"))
au.central.fem <- droplevels(subset(au.central,sexe=="F"))au.central.mas$ton.ord <- as.ordered(au.central.mas$ton)
contrasts(au.central.mas$ton.ord) <- "contr.treatment"
au.central.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 550.448 9.241 59.564 < 2e-16 ***
## ton.ord2 129.179 15.383 8.397 2.34e-16 ***
## ton.ord3 127.691 11.019 11.588 < 2e-16 ***
## ton.ord4 118.533 9.796 12.100 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.810 3.396 15.852 < 2e-16 ***
## s(measurement.no):ton.ord2 1.003 1.005 4.378 0.03641 *
## s(measurement.no):ton.ord3 1.001 1.001 2.404 0.12136
## s(measurement.no):ton.ord4 1.000 1.000 9.126 0.00261 **plot_smooth(au.central.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 8.000000plot_diff(au.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(au.central.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 4.121212au.central.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 546.970 8.750 62.510 <2e-16 ***
## ton.ord2 126.248 14.702 8.587 <2e-16 ***
## ton.ord3 125.939 10.419 12.088 <2e-16 ***
## ton.ord4 124.633 9.313 13.383 <2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.889 3.483 16.396 < 2e-16 ***
## s(duree.ms.) 4.729 4.956 12.542 < 2e-16 ***
## ti(measurement.no,duree.ms.) 1.007 1.014 25.808 5.65e-07 ***
## s(measurement.no):ton.ord2 1.001 1.002 7.021 0.00819 **
## s(measurement.no):ton.ord3 1.001 1.001 2.557 0.11019
## s(measurement.no):ton.ord4 1.001 1.002 6.929 0.00865 **plot_smooth(au.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.central.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 88.249203 to 188.623093.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.central.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 556.694 9.629 57.813 < 2e-16 ***
## ton.ord2 126.541 15.180 8.336 5.20e-16 ***
## ton.ord3 94.060 12.558 7.490 2.45e-13 ***
## ton.ord4 103.838 10.329 10.053 < 2e-16 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.847 3.437 9.980 1.38e-06 ***
## s(f0) 3.726 4.190 9.061 5.58e-07 ***
## ti(measurement.no,f0) 2.223 2.733 9.811 9.87e-06 ***
## s(measurement.no):ton.ord2 1.003 1.006 1.007 0.317
## s(measurement.no):ton.ord3 1.000 1.001 0.636 0.426
## s(measurement.no):ton.ord4 1.001 1.001 0.356 0.551plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.central.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 96.144383 to 194.306588.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2.1.2 F2
Now we look at the trajectories of f2 in different tones with regard of the sexes and the durations.
ggplot(au.mas, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 28 row(s) containing missing values (geom_path).
ggplot(au.fem, aes(x=measurement.no, y=f2, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 5 row(s) containing missing values (geom_path).
2.1.2.1 Basic models
au.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1060.38 19.25 55.073 < 2e-16 ***
## ton.ord2 -16.26 31.91 -0.509 0.61057
## ton.ord3 41.68 22.95 1.816 0.06963 .
## ton.ord4 71.39 20.42 3.496 0.00049 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.749 5.770 22.857 <2e-16 ***
## s(measurement.no):ton.ord2 1.001 1.002 1.953 0.162
## s(measurement.no):ton.ord3 1.001 1.002 0.359 0.549
## s(measurement.no):ton.ord4 1.001 1.002 0.525 0.469Now the plots of f2 with different tones.
plot_smooth(au.mas.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.plot_diff(au.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 5.050505plot_diff(au.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.939394 - 6.161616The model that accounts for the influence of duree.ms. on the trajectories.
au.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1063.07 18.99 55.986 < 2e-16 ***
## ton.ord2 -17.43 31.58 -0.552 0.580999
## ton.ord3 39.56 22.57 1.753 0.079956 .
## ton.ord4 68.74 20.20 3.404 0.000689 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.777 5.801 23.811 < 2e-16 ***
## s(duree.ms.) 2.383 2.983 3.122 0.0298 *
## ti(measurement.no,duree.ms.) 3.868 5.468 5.791 1.4e-05 ***
## s(measurement.no):ton.ord2 1.001 1.002 3.162 0.0755 .
## s(measurement.no):ton.ord3 1.001 1.002 0.258 0.6123
## s(measurement.no):ton.ord4 1.001 1.002 0.032 0.8598The plots with regard the durations.
plot_smooth(au.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 88.249203 to 188.623093.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.mas, method="ML")
summary.coefs(au.mas.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1040.123 21.482 48.418 < 2e-16 ***
## ton.ord2 1.004 33.381 0.030 0.9760
## ton.ord3 57.854 28.533 2.028 0.0429 *
## ton.ord4 106.077 23.094 4.593 4.98e-06 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.474 5.466 14.610 < 2e-16 ***
## s(f0) 3.770 4.423 3.068 0.01447 *
## ti(measurement.no,f0) 5.973 7.372 3.161 0.00211 **
## s(measurement.no):ton.ord2 1.002 1.005 1.194 0.27402
## s(measurement.no):ton.ord3 1.002 1.003 3.514 0.06108 .
## s(measurement.no):ton.ord4 1.001 1.003 0.329 0.56735plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.mas.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 96.765573 to 193.084157.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2.1.2.2 Central portion
The central portion:
au.central.mas.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1019.65 17.72 57.550 < 2e-16 ***
## ton.ord2 -28.96 29.49 -0.982 0.326539
## ton.ord3 41.91 21.13 1.984 0.047634 *
## ton.ord4 72.29 18.78 3.849 0.000129 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.436 2.974 5.628 0.000806 ***
## s(measurement.no):ton.ord2 1.001 1.001 0.060 0.806948
## s(measurement.no):ton.ord3 1.001 1.002 1.600 0.205982
## s(measurement.no):ton.ord4 1.003 1.005 1.718 0.189273plot_smooth(au.central.mas.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(au.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.878788 - 8.000000plot_diff(au.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.575758 - 6.060606plot_diff(au.central.mas.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.424242 - 8.000000au.central.mas.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1023.66 17.02 60.138 < 2e-16 ***
## ton.ord2 -27.88 28.47 -0.979 0.327697
## ton.ord3 38.52 20.25 1.902 0.057516 .
## ton.ord4 67.71 18.10 3.741 0.000198 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.535 3.088 5.539 0.00085 ***
## s(duree.ms.) 3.040 3.634 10.338 6.04e-07 ***
## ti(measurement.no,duree.ms.) 1.008 1.015 31.035 < 2e-16 ***
## s(measurement.no):ton.ord2 1.000 1.001 0.413 0.52098
## s(measurement.no):ton.ord3 1.001 1.001 1.316 0.25143
## s(measurement.no):ton.ord4 1.000 1.001 0.553 0.45724plot_smooth(au.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.mas.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.central.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 88.249203 to 188.623093.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.central.mas.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.mas, method="ML")
summary.coefs(au.central.mas.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1001.57 19.59 51.118 < 2e-16 ***
## ton.ord2 -11.55 30.90 -0.374 0.70875
## ton.ord3 66.99 25.01 2.679 0.00759 **
## ton.ord4 108.92 21.06 5.171 3.16e-07 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.906 2.355 3.173 0.0343 *
## s(f0) 1.000 1.000 4.531 0.0337 *
## ti(measurement.no,f0) 2.748 3.204 3.803 0.0104 *
## s(measurement.no):ton.ord2 1.000 1.001 0.003 0.9624
## s(measurement.no):ton.ord3 1.000 1.001 3.746 0.0533 .
## s(measurement.no):ton.ord4 1.004 1.007 1.428 0.2338plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.mas.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.mas.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 96.765573 to 193.084157.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2.2 Féminin
2.2.1 F1
2.2.1.1 Basic models
We now switch to the data of feminin subjects.
The first model with a basic smooth of tone 1 and difference smooths.
au.fem$ton.ord <- as.ordered(au.fem$ton)
contrasts(au.fem$ton.ord) <- "contr.treatment"
au.fem.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.fem, method="ML")
summary.coefs(au.fem.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 705.06 10.06 70.066 < 2e-16 ***
## ton.ord2 187.78 33.38 5.626 2.96e-08 ***
## ton.ord3 62.30 16.43 3.791 0.000167 ***
## ton.ord4 81.91 11.47 7.144 2.94e-12 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.740 5.758 43.537 < 2e-16 ***
## s(measurement.no):ton.ord2 3.198 3.954 5.294 0.000381 ***
## s(measurement.no):ton.ord3 1.840 2.291 1.256 0.298494
## s(measurement.no):ton.ord4 1.002 1.003 7.957 0.004933 **Then the plots of predictions and difference smooth.
plot_smooth(au.fem.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 1.212121 - 4.444444
## 6.767677 - 10.000000plot_diff(au.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 7.777778 - 10.000000plot_diff(au.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 5.151515 - 7.373737The model that accounts for the influence of duree.ms. on the trajectories.
au.fem.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.fem, method="ML")
summary.coefs(au.fem.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 703.912 9.631 73.085 < 2e-16 ***
## ton.ord2 162.616 33.082 4.916 1.18e-06 ***
## ton.ord3 71.044 16.139 4.402 1.30e-05 ***
## ton.ord4 83.049 11.045 7.519 2.38e-13 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.857 5.888 47.913 < 2e-16 ***
## s(duree.ms.) 7.252 8.033 6.097 < 2e-16 ***
## ti(measurement.no,duree.ms.) 4.766 6.124 4.095 0.000464 ***
## s(measurement.no):ton.ord2 3.249 4.016 5.877 0.000122 ***
## s(measurement.no):ton.ord3 2.040 2.538 1.656 0.178389
## s(measurement.no):ton.ord4 1.002 1.003 8.829 0.003075 **The plots with regard the durations.
plot_smooth(au.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.fem.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 97.219130 to 204.993095.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
au.fem.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.fem, method="ML")
summary.coefs(au.fem.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 712.08 10.12 70.351 < 2e-16 ***
## ton.ord2 124.01 30.67 4.043 6.13e-05 ***
## ton.ord3 45.52 18.08 2.518 0.0121 *
## ton.ord4 75.80 11.95 6.341 5.21e-10 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 5.691 6.795 66.027 < 2e-16 ***
## s(f0) 3.990 4.966 7.738 7.61e-07 ***
## ti(measurement.no,f0) 1.001 1.002 4.710 0.03037 *
## s(measurement.no):ton.ord2 3.554 4.382 10.537 < 2e-16 ***
## s(measurement.no):ton.ord3 1.001 1.002 6.506 0.01100 *
## s(measurement.no):ton.ord4 1.001 1.002 9.902 0.00175 **The plot of such model.
plot_smooth(au.fem.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.fem.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 148.879493 to 290.377970.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2.2.1.2 Central portion
We now focus on the central portion of the diphthongs, which means the portions without the inluence of the consonant contexts.
au.central.fem$ton.ord <- as.ordered(au.central.fem$ton)
contrasts(au.central.fem$ton.ord) <- "contr.treatment"
au.central.fem.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.fem, method="ML")
summary.coefs(au.central.fem.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 756.899 9.062 83.529 < 2e-16 ***
## ton.ord2 124.447 30.054 4.141 4.35e-05 ***
## ton.ord3 40.090 14.797 2.709 0.00708 **
## ton.ord4 75.388 10.308 7.313 1.82e-12 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.899 3.493 15.569 <2e-16 ***
## s(measurement.no):ton.ord2 1.000 1.001 0.130 0.7195
## s(measurement.no):ton.ord3 1.000 1.001 0.885 0.3473
## s(measurement.no):ton.ord4 1.000 1.001 4.559 0.0334 *plot_smooth(au.central.fem.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 8.000000plot_diff(au.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 2.000000 - 6.121212plot_diff(au.central.fem.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.696970 - 8.000000au.central.fem.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.fem, method="ML")
summary.coefs(au.central.fem.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 759.352 8.740 86.885 < 2e-16 ***
## ton.ord2 132.451 29.078 4.555 7.29e-06 ***
## ton.ord3 41.184 14.296 2.881 0.00422 **
## ton.ord4 71.279 9.988 7.137 5.74e-12 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.943 3.542 16.051 < 2e-16 ***
## s(duree.ms.) 2.429 2.901 4.261 0.008022 **
## ti(measurement.no,duree.ms.) 1.913 2.312 8.000 0.000239 ***
## s(measurement.no):ton.ord2 1.000 1.001 0.049 0.825277
## s(measurement.no):ton.ord3 1.001 1.001 0.387 0.534156
## s(measurement.no):ton.ord4 1.001 1.001 4.180 0.041654 *plot_smooth(au.central.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.fem.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.central.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 97.219130 to 204.993095.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.central.fem.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.fem, method="ML")
summary.coefs(au.central.fem.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 756.85 10.62 71.252 < 2e-16 ***
## ton.ord2 62.20 32.49 1.914 0.0565 .
## ton.ord3 45.61 18.32 2.489 0.0133 *
## ton.ord4 79.88 12.39 6.445 4.14e-10 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.922 3.520 19.621 < 2e-16 ***
## s(f0) 3.812 4.432 7.654 5.98e-06 ***
## ti(measurement.no,f0) 1.006 1.013 7.034 0.00807 **
## s(measurement.no):ton.ord2 1.001 1.001 1.251 0.26405
## s(measurement.no):ton.ord3 1.000 1.000 7.390 0.00691 **
## s(measurement.no):ton.ord4 1.000 1.000 8.708 0.00339 **plot_smooth(au.central.fem.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.fem.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.central.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 148.704236 to 283.580290.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2.2.2 F2
2.2.2.1 Basic models
We fit the same model with a basic smooth of tone 1 and difference smooths.
au.fem.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.fem, method="ML")
summary.coefs(au.fem.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1328.42 17.10 77.689 <2e-16 ***
## ton.ord2 -13.33 56.72 -0.235 0.8142
## ton.ord3 57.08 27.92 2.044 0.0414 *
## ton.ord4 36.30 19.48 1.863 0.0629 .
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.212 5.157 20.893 < 2e-16 ***
## s(measurement.no):ton.ord2 3.288 4.063 3.777 0.00447 **
## s(measurement.no):ton.ord3 1.003 1.007 3.779 0.05239 .
## s(measurement.no):ton.ord4 1.002 1.003 0.082 0.77608Now the plots of f2 with different tones.
plot_smooth(au.fem.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 8.989899 - 10.000000plot_diff(au.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 8.989899 - 10.000000plot_diff(au.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.000000 - 2.222222The model that accounts for the influence of duree.ms. on the trajectories.
au.fem.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.fem, method="ML")
summary.coefs(au.fem.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1328.94 16.23 81.863 <2e-16 ***
## ton.ord2 -12.55 53.84 -0.233 0.8157
## ton.ord3 51.30 26.61 1.928 0.0544 .
## ton.ord4 37.07 18.49 2.004 0.0455 *
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.348 5.314 23.431 < 2e-16 ***
## s(duree.ms.) 1.001 1.002 6.013 0.0145 *
## ti(measurement.no,duree.ms.) 8.917 11.250 4.971 1.08e-07 ***
## s(measurement.no):ton.ord2 3.165 3.913 2.851 0.0193 *
## s(measurement.no):ton.ord3 1.003 1.005 5.069 0.0247 *
## s(measurement.no):ton.ord4 1.001 1.002 0.276 0.5996The plots with regard the durations.
plot_smooth(au.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.fem.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 97.219130 to 204.993095.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.fem.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=au.fem, method="ML")
summary.coefs(au.fem.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1306.74 19.50 67.019 <2e-16 ***
## ton.ord2 57.97 58.31 0.994 0.3206
## ton.ord3 78.41 34.58 2.267 0.0238 *
## ton.ord4 57.03 23.21 2.457 0.0144 *
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 4.315 5.286 21.591 < 2e-16 ***
## s(f0) 5.489 6.519 4.799 6.23e-05 ***
## ti(measurement.no,f0) 1.128 1.242 0.208 0.81693
## s(measurement.no):ton.ord2 3.704 4.561 3.412 0.00568 **
## s(measurement.no):ton.ord3 1.000 1.001 0.404 0.52539
## s(measurement.no):ton.ord4 1.001 1.001 1.031 0.31041plot_smooth(au.fem.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.f2.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.f2.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.fem.f2.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.fem.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 148.879493 to 290.377970.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
2.2.2.2 Central portion
The central portion:
au.central.fem.f2.gam.diff <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.fem, method="ML")
summary.coefs(au.central.fem.f2.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1276.24 15.67 81.426 <2e-16 ***
## ton.ord2 -114.80 51.98 -2.208 0.0279 *
## ton.ord3 48.00 25.59 1.875 0.0616 .
## ton.ord4 38.37 17.83 2.152 0.0321 *
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.801 3.387 7.081 7.2e-05 ***
## s(measurement.no):ton.ord2 1.001 1.003 0.307 0.580
## s(measurement.no):ton.ord3 1.001 1.002 0.019 0.893
## s(measurement.no):ton.ord4 1.001 1.002 0.147 0.702plot_smooth(au.central.fem.f2.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(au.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 4.424242 - 6.969697plot_diff(au.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.272727 - 8.000000plot_diff(au.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## Difference is not significant.plot_diff(au.central.fem.f2.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 2.000000 to 8.000000.
##
## measurement.no window(s) of significant difference(s):
## 3.454545 - 8.000000au.central.fem.f2.gam.dur <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(duree.ms., bs="cr",k=6) +
ti(measurement.no, duree.ms.,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.fem, method="ML")
summary.coefs(au.central.fem.f2.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1282.40 14.45 88.740 <2e-16 ***
## ton.ord2 -91.07 48.32 -1.885 0.0603 .
## ton.ord3 39.68 23.65 1.678 0.0942 .
## ton.ord4 29.89 16.54 1.807 0.0717 .
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.903 3.498 8.598 7.34e-06 ***
## s(duree.ms.) 3.207 3.748 13.153 < 2e-16 ***
## ti(measurement.no,duree.ms.) 4.101 4.584 3.416 0.00422 **
## s(measurement.no):ton.ord2 1.001 1.001 0.147 0.70186
## s(measurement.no):ton.ord3 1.000 1.001 0.206 0.65087
## s(measurement.no):ton.ord4 1.000 1.001 0.621 0.43104plot_smooth(au.central.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.f2.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.fem.f2.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(au.central.fem$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 97.219130 to 204.993095.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
au.central.fem.f2.gam.f0 <- bam(f2 ~ ton.ord + s(measurement.no, bs="cr",k=6) +
s(f0, bs="cr",k=6) +
ti(measurement.no, f0,k=6) +
s(measurement.no, by=ton.ord, bs="cr",k=6),
data=au.central.fem, method="ML")
summary.coefs(au.central.fem.f2.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1252.48 19.43 64.458 < 2e-16 ***
## ton.ord2 -16.17 58.95 -0.274 0.78408
## ton.ord3 95.71 33.35 2.869 0.00438 **
## ton.ord4 67.61 22.79 2.967 0.00323 **
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 2.824 3.414 7.533 3.79e-05 ***
## s(f0) 4.509 4.883 3.847 0.00131 **
## ti(measurement.no,f0) 1.000 1.000 1.717 0.19101
## s(measurement.no):ton.ord2 1.007 1.014 0.035 0.86410
## s(measurement.no):ton.ord3 1.000 1.000 1.616 0.20448
## s(measurement.no):ton.ord4 1.000 1.000 1.401 0.23747plot_smooth(au.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=220),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 220.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=240),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 240.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(au.central.fem.f2.gam.f0, view="measurement.no", cond=list(f0=260),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; set to the value(s): 260.
## * NOTE : No random effects in the model to cancel.
## fvisgam(au.central.fem.f2.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(au.central.fem$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 4.
## * measurement.no : numeric predictor; with 30 values ranging from 2.000000 to 8.000000.
## * f0 : numeric predictor; with 30 values ranging from 148.704236 to 283.580290.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
3 /ei/
The third one is diphthong /ei/.
ei$sexe<-as.factor(ei$sexe)
ei$ton<-as.factor(ei$ton)
ei$pow<-as.factor(ei$pow)
ei$contexte.D<-as.factor(ei$contexte.D)
ei$contexte.G<-as.factor(ei$contexte.G)
ei$f1<-as.numeric(ei$f1)## Warning: NAs introduced by coercionei$f2<-as.numeric(ei$f2)## Warning: NAs introduced by coercionei$f3<-as.numeric(ei$f3)## Warning: NAs introduced by coercionei$f0<-as.numeric(ei$f0)## Warning: NAs introduced by coercion# Regroupement par les facteurs
ei.mas <- droplevels(subset(ei,sexe=="M"))
ei.fem <- droplevels(subset(ei,sexe=="F"))3.1 Masculin
3.1.1 F1
Then the trajectories of f1 in different tones with regard of the sexes and the durations.
ggplot(ei.mas, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 17 row(s) containing missing values (geom_path).
ggplot(ei.fem, aes(x=measurement.no, y=f1, group=numero,
alpha=duree.ms.)) +
facet_grid(~ton) + geom_line()## Warning: Removed 5 row(s) containing missing values (geom_path).
The basic model with the tone.
ei.mas$ton.ord <- as.ordered(ei.mas$ton)
contrasts(ei.mas$ton.ord) <- "contr.treatment"
ei.mas.gam.diff <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(measurement.no, by=ton.ord, bs="cr"),
data=ei.mas, method="ML")
summary.coefs(ei.mas.gam.diff)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 382.24 21.92 17.440 < 2e-16 ***
## ton.ord2 15.28 26.52 0.576 0.564521
## ton.ord3 80.97 23.54 3.439 0.000604 ***
## ton.ord4 96.06 24.49 3.922 9.27e-05 ***Then the plots of predictions and difference smooth.
plot_smooth(ei.mas.gam.diff, view="measurement.no",
plot_all="ton.ord", rug=F)## Summary:
## * ton.ord : factor; set to the value(s): 1, 2, 3, 4.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * NOTE : No random effects in the model to cancel.
## 
plot_diff(ei.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("1","2")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.plot_diff(ei.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("2","3")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## measurement.no window(s) of significant difference(s):
## 0.505051 - 8.181818plot_diff(ei.mas.gam.diff, view="measurement.no",
comp=list(ton.ord=c("3","4")))## Summary:
## * measurement.no : numeric predictor; with 100 values ranging from 0.000000 to 10.000000.
##
## Difference is not significant.The model that accounts for the influence of duree.ms. on the trajectories.
ei.mas.gam.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ei.mas, method="ML")
summary.coefs(ei.mas.gam.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 383.014 22.572 16.969 < 2e-16 ***
## ton.ord2 2.031 27.687 0.073 0.941525
## ton.ord3 90.245 24.282 3.717 0.000211 ***
## ton.ord4 85.518 25.448 3.361 0.000803 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.006 1.011 0.711 0.3988
## s(duree.ms.) 7.575 8.320 8.362 <2e-16 ***
## ti(measurement.no,duree.ms.) 5.104 6.914 2.222 0.0305 *
## s(measurement.no):ton.ord2 2.143 2.663 0.964 0.3046
## s(measurement.no):ton.ord3 1.471 1.798 0.207 0.7371
## s(measurement.no):ton.ord4 1.005 1.010 1.189 0.2746The plots with regard the durations.
plot_smooth(ei.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=170),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 170.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.dur, view="measurement.no", cond=list(duree.ms.=80),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; set to the value(s): 80.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ei.mas.gam.dur, view=c("measurement.no","duree.ms."),
ylim=quantile(ei.mas$duree.ms., c(0.1, 0.9)))## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * duree.ms. : numeric predictor; with 30 values ranging from 69.653645 to 160.541647.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
The model with regard of f0.
ei.mas.gam.f0 <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ei.mas, method="ML")
summary.coefs(ei.mas.gam.f0)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 399.41 22.83 17.494 < 2e-16 ***
## ton.ord2 17.73 27.32 0.649 0.516427
## ton.ord3 51.91 25.31 2.051 0.040519 *
## ton.ord4 97.15 25.32 3.837 0.000131 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.002 1.003 1.014 0.3142
## s(f0) 5.427 6.335 7.715 <2e-16 ***
## ti(measurement.no,f0) 2.687 3.138 2.545 0.0699 .
## s(measurement.no):ton.ord2 2.055 2.568 1.245 0.2285
## s(measurement.no):ton.ord3 1.003 1.006 0.006 0.9567
## s(measurement.no):ton.ord4 1.002 1.003 2.035 0.1536The plot of such model.
plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ei.mas.gam.f0, view=c("measurement.no","f0"),
ylim=quantile(ei.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 92.830073 to 209.388440.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
ei.mas.gam.f0.dur <- bam(f1 ~ ton.ord + s(measurement.no, bs="cr") +
s(f0, bs="cr") +
ti(measurement.no, f0) +
s(duree.ms., bs="cr") +
ti(measurement.no, duree.ms.) +
s(measurement.no, by=ton.ord, bs="cr"),
data=ei.mas, method="ML")
summary.coefs(ei.mas.gam.f0.dur)## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 391.24 23.22 16.853 < 2e-16 ***
## ton.ord2 15.12 28.39 0.532 0.594501
## ton.ord3 70.49 25.83 2.729 0.006447 **
## ton.ord4 96.54 26.13 3.695 0.000231 ***
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(measurement.no) 1.002 1.004 2.001 0.1573
## s(f0) 5.595 6.509 7.350 <2e-16 ***
## ti(measurement.no,f0) 2.900 3.338 3.492 0.0267 *
## s(duree.ms.) 7.761 8.457 9.119 <2e-16 ***
## ti(measurement.no,duree.ms.) 5.515 7.444 1.983 0.0539 .
## s(measurement.no):ton.ord2 2.300 2.862 2.052 0.0837 .
## s(measurement.no):ton.ord3 1.003 1.006 0.099 0.7580
## s(measurement.no):ton.ord4 1.002 1.003 1.069 0.3013plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=100),
rug=F, col="red")## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 100.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=120),
rug=F, col="orange", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 120.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=140),
rug=F, col="yellow", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 140.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=180),
rug=F, col="green", add=T)## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 180.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## plot_smooth(ei.mas.gam.f0.dur, view="measurement.no", cond=list(f0=200),
rug=F, col="blue", add=T)
## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; set to the value(s): 200.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## fvisgam(ei.mas.gam.f0.dur, view=c("measurement.no","f0"),
ylim=quantile(ei.mas$f0, c(0.1, 0.9), na.rm=TRUE))## Summary:
## * ton.ord : factor; set to the value(s): 3.
## * measurement.no : numeric predictor; with 30 values ranging from 0.000000 to 10.000000.
## * f0 : numeric predictor; with 30 values ranging from 92.830073 to 209.388440.
## * duree.ms. : numeric predictor; set to the value(s): 106.033100625903.
## * NOTE : No random effects in the model to cancel.
## ## Warning in gradientLegend(c(min.z, max.z), n.seg = 3, pos = 0.875, color =
## pal, : Increase right margin to fit labels or decrease the number of decimals,
## see help(gradientLegend).
4 Analysis
4.1 Factor duration
The influence of the factor duration is commun in all the diphthongs. All the diphthongs will be realized as more monophthongized with a brief duration.
4.2 Factor f0
The General influence of the factor of f0 on the f1 and f2 is as such:
f0 and f1 is a negative correlation.
f0 and f2 is a positive correlation.
However, this correlation is influenced by other factors and not on the same level within the different diphthongs.
In diphthong /ai/, the correlation between f0 and f1 is positive within the female data, which should be regarded after.